[代码资源] 用对分法解超越方程

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发表于 2016-10-12 23:05 |只看该作者 |倒序浏览

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范例：用对分法求方程在(0,1)内的根，要求误差不超过0.1；
求解程序如下：

clear;clc;close$ k; {- _2 G# |8 S5 b
% n=input('请输入迭代次数：');( h$ e1 I# c0 P7 B
% qujian=input('请输入初始区间：'); `$ N2 M0 v! I$ t- Y! r$ K
n=100;
: Q) F9 P7 A; T& g7 m# h) L! v
wucha=0.005;
. D$ v( m9 L7 u7 x* @+ b
qujian=[0 1];; y8 }8 o0 B+ o3 e/ f+ O# s
a(1)=qujian(1);
2 f% i; W# A9 u$ Q
b(1)=qujian(2);
* z, }6 }! u6 A
a0=a(1);
# d( d; e8 E q( R4 l\" [* Y
b0=b(1);
1 v/ E+ o2 R* L: h$ C
x=qujian;4 u* c& u' \& N# h
y=exp(x)+10*x-2;
, T& i9 o: T. Z* E8 \ e
y1=y(1); %小于0
' O8 X8 v) u5 K6 t; C
y2=y(2); %大于0( W2 ?0 `) L8 {$ E4 G
for i=1:n %总迭代次数
* L% y3 O& z. d
c(i)=(a+b)/2;, }: O7 V1 J' ^
f(i)=exp(c(i))+10*(c(i))-2;: h$ c+ X9 i& L5 P
kesai_k(i)=(b-a)/2;
' I9 |: P, ? b+ w4 b
if f(i)>0
% f8 X# d0 ^$ f; Q
b=c(i);0 O7 S! S+ \$ P9 u' q
b1(i)=c(i);
$ {! X. F; o* y- \5 ?# V; t
a1(i)=a;
7 [# p) E; ?- N8 Q8 a+ O3 K
elseif f(i)<0. _1 e- T9 w2 u1 U, T5 ~/ e
a=c(i);
8 h w# O0 j* K) a' m$ E
a1(i)=c(i);1 C! W# \/ t. A7 _$ ]
b1(i)=b;
. g3 S- c; x) {2 U/ J/ [
elseif f(i)==0||kesai_k(i)<=wucha7 Z/ C! c6 {1 _& u2 R0 }7 B
disp('精确值解为：');) ^$ A, w# B( b* C! d& N c$ [+ E9 }
disp(c(i));
\" z' y% s- J/ F4 t0 e/ _( V: K
break;& Z1 |! P T- ]5 ?, z v2 H, Q
end
. i; e\" f4 g/ u, N
end
! C ~( W7 ?1 T: e( c
disp('迭代次数：');' h/ u# w/ g3 f0 M4 Z0 a: t
fprintf('%d次\n\n',n);
- P$ {3 G- k+ B) s3 @7 E( Q
fprintf('要求误差%f\n\n',wucha);
! D! R# Q4 X% k3 Z1 o2 E1 x7 f
disp('输出矩阵为：');
* {$ {/ _& P, a9 i( U c
A=[a0 a1]';) H& ^2 q* M8 T2 n; L0 [
B=[b0 b1]';
3 \0 V0 a7 } @* j
format long
7 B, i+ v' o/ o! J% ~4 i, r
data_out=[A B c' f' kesai_k']
W\" ^; ]' R1 `$ X3 I e
xlswrite('二分法处理数据.xls',data_out);

复制代码

结果输出情况：

精确值解为：
' f5 m+ C5 M: N% X' `
0.0905& _6 Z' {8 t5 i5 k
+ R$ A( e. e; |0 F2 h% Z: w# r+ ?
迭代次数：
$ p9 Z1 P# }$ ]* t
100次
8 W6 K- y. M7 d
: g: N& A, p% t, H. R& C2 r4 @
要求误差0.005000; J- r. r3 k- W J( N0 c2 k
) `: d' s$ G( O) V& e8 M1 X
输出矩阵为：
1 L& L5 S3 r( F0 I4 ~5 o( }
9 k5 r' K$ s, U4 S+ e2 `
data_out =
0 T8 ^% y8 v3 O# m
. M- c7 j7 F; u q
0 1.000000000000000 0.500000000000000 4.648721270700128 0.500000000000000% i. `& n+ q% ?
0 0.500000000000000 0.250000000000000 1.784025416687741 0.250000000000000 z% ~8 u, ~' V+ r2 e' s
0 0.250000000000000 0.125000000000000 0.383148453066826 0.125000000000000
( {% b H+ U4 c% n
0 0.125000000000000 0.062500000000000 -0.310505541082140 0.062500000000000
1 x! w+ v8 v! T# @2 x: w9 G2 G
0.062500000000000 0.125000000000000 0.093750000000000 0.035785140307826 0.031250000000000; J) j2 T: Q4 m6 F7 `! I) q5 Q- _
0.062500000000000 0.093750000000000 0.078125000000000 -0.137492192550960 0.015625000000000
/ k! C3 s1 \1 p& r6 M
0.078125000000000 0.093750000000000 0.085937500000000 -0.050886782461907 0.007812500000000/ f! n\" u6 E0 O3 Q/ x
0.085937500000000 0.093750000000000 0.089843750000000 -0.007559167670695 0.003906250000000
6 f* ^9 k6 J. m& |* f
0.089843750000000 0.093750000000000 0.091796875000000 0.014110895592678 0.001953125000000
: K5 M5 e1 U% J0 U/ {! P
0.089843750000000 0.091796875000000 0.090820312500000 0.003275341789827 0.000976562500000# b9 J: u8 g0 J% ^5 Y( G
0.089843750000000 0.090820312500000 0.090332031250000 -0.002142043419492 0.0004882812500002 v/ \+ Z1 r& T
0.090332031250000 0.090820312500000 0.090576171875000 0.000566616557439 0.000244140625000
$ [/ f, i\" N1 J
0.090332031250000 0.090576171875000 0.090454101562500 -0.000787721586963 0.0001220703125008 p3 W+ B% W* u. R
0.090454101562500 0.090576171875000 0.090515136718750 -0.000110554553871 0.000061035156250! l( D9 r+ W9 `2 H4 Z5 O7 ]8 L9 J
0.090515136718750 0.090576171875000 0.090545654296875 0.000228030491991 0.000030517578125
: ~5 I- p+ J6 u1 H
0.090515136718750 0.090545654296875 0.090530395507813 0.000058737841614 0.000015258789063
8 {. Q\" P) _. `9 F! ?; r& F
0.090515136718750 0.090530395507813 0.090522766113281 -0.000025908387990 0.000007629394531( c+ m! v+ X9 g3 S- d
0.090522766113281 0.090530395507813 0.090526580810547 0.000016414718847 0.000003814697266/ `\" g; @+ y4 S* ^9 p0 a
0.090522766113281 0.090526580810547 0.090524673461914 -0.000004746836563 0.000001907348633
/ }2 E\" S0 I- r: Z. X n
0.090524673461914 0.090526580810547 0.090525627136230 0.000005833940644 0.000000953674316
8 m, w# m: f$ D9 j# V2 Q6 [
0.090524673461914 0.090525627136230 0.090525150299072 0.000000543551916 0.000000476837158
4 O+ c. h& G. e! m
0.090524673461914 0.090525150299072 0.090524911880493 -0.000002101642354 0.000000238418579% X9 Q: ?) i0 ~, B
0.090524911880493 0.090525150299072 0.090525031089783 -0.000000779045227 0.000000119209290
$ t. c+ y* a, F: ~/ M' K
0.090525031089783 0.090525150299072 0.090525090694427 -0.000000117746657 0.000000059604645
6 s9 i) g+ b% N8 W; \3 u$ ?
0.090525090694427 0.090525150299072 0.090525120496750 0.000000212902629 0.000000029802322
& }( n+ {! ~/ R
0.090525090694427 0.090525120496750 0.090525105595589 0.000000047577986 0.0000000149011617 h% h# A7 K# Y2 \6 ?/ l$ r
0.090525090694427 0.090525105595589 0.090525098145008 -0.000000035084336 0.000000007450581, r& U& _4 S4 x {) G
0.090525098145008 0.090525105595589 0.090525101870298 0.000000006246825 0.0000000037252905 G7 f; k5 G( l$ ? z( e8 e7 j; C1 m
0.090525098145008 0.090525101870298 0.090525100007653 -0.000000014418755 0.0000000018626452 u8 F$ U. b8 [ |, W( c( e
0.090525100007653 0.090525101870298 0.090525100938976 -0.000000004085965 0.000000000931323
- P9 o\" A2 l$ s0 ?( f\" }( d% G) p
0.090525100938976 0.090525101870298 0.090525101404637 0.000000001080430 0.000000000465661; ^) v; a7 |$ {& q H4 o
0.090525100938976 0.090525101404637 0.090525101171806 -0.000000001502767 0.0000000002328310 s2 `9 O$ a% c+ h- g
0.090525101171806 0.090525101404637 0.090525101288222 -0.000000000211169 0.000000000116415
1 {\" _3 @0 `$ C1 ~1 v0 s; W
0.090525101288222 0.090525101404637 0.090525101346429 0.000000000434631 0.0000000000582081 _/ Y6 z/ ~& ^2 H |1 [. O) j! E
0.090525101288222 0.090525101346429 0.090525101317326 0.000000000111731 0.000000000029104
7 ~8 \, R6 D\" }4 B1 m' r* X9 p, v- L
0.090525101288222 0.090525101317326 0.090525101302774 -0.000000000049719 0.000000000014552
& O# q' s7 m$ J! b9 e
0.090525101302774 0.090525101317326 0.090525101310050 0.000000000031006 0.0000000000072766 s d% r$ O- ^, K
0.090525101302774 0.090525101310050 0.090525101306412 -0.000000000009357 0.000000000003638, l: [( X) x6 S0 V0 }
0.090525101306412 0.090525101310050 0.090525101308231 0.000000000010825 0.000000000001819
4 _. G a8 R9 D% _3 \
0.090525101306412 0.090525101308231 0.090525101307321 0.000000000000734 0.000000000000909
$ G8 [0 R/ Y; a& j5 m8 S
0.090525101306412 0.090525101307321 0.090525101306866 -0.000000000004311 0.000000000000455
5 B9 W' W0 A, g$ R* }
0.090525101306866 0.090525101307321 0.090525101307094 -0.000000000001789 0.000000000000227
( p: J0 @$ F' Z& X
0.090525101307094 0.090525101307321 0.090525101307207 -0.000000000000527 0.000000000000114
! H: F+ L( s: }9 V
0.090525101307207 0.090525101307321 0.090525101307264 0.000000000000103 0.000000000000057
) B1 K2 B5 V\" u2 d, x5 o
0.090525101307207 0.090525101307264 0.090525101307236 -0.000000000000212 0.000000000000028
2 f% G( C6 v. ]
0.090525101307236 0.090525101307264 0.090525101307250 -0.000000000000054 0.000000000000014+ J [ r$ N3 d
0.090525101307250 0.090525101307264 0.090525101307257 0.000000000000025 0.0000000000000072 Q8 B\" h1 Z- {5 j1 f6 e
0.090525101307250 0.090525101307257 0.090525101307254 -0.000000000000015 0.000000000000004! y% \( G! C$ Z7 x/ ?0 {- y( C( s. e
0.090525101307254 0.090525101307257 0.090525101307255 0.000000000000005 0.000000000000002/ {1 E$ C% f9 ?; k% T( e Q. X4 o$ j
0.090525101307254 0.090525101307255 0.090525101307255 -0.000000000000005 0.0000000000000013 c5 c9 \$ ~\" ^7 V: o, d1 J
0.090525101307255 0.090525101307255 0.090525101307255 0 0.000000000000000